1. Field of the Invention
This invention relates to a transformer for voltage regulators, and more particularly to a novel transformer suitable for use in a constant voltage circuit which is formed by combination of a saturable transformer and a switching regulator.
2. Description of the Prior Art
This application is an improvement of my copending application, Ser. No. 138,341 filed Apr. 8, 1980 for "Voltage Regulator Using Saturable Transformer".
Now, a consideration will be taken into a transformer as shown in FIG. 1, in which 10 designates the transformer as a whole. Transformer 10 includes a pair of magnetic cores 11 and 12 made of ferrite, each having a base portion 10E in a shape of, for example, square plate and legs 10A, 10B, 10C and 10D respectively erected vertically from four corners of base 10E. Respective legs 10A to 10D have the same sectional area. Core 11 is arranged in opposition to core 12 in such a manner that each leg of the former may contact at its end with that of the latter. Accordingly, cores 11 and 12 are assembled in a shape of a cube or rectangular parallelepiped as a whole.
A primary winding (exciting winding) N.sub.1 is wound spreading over legs 10B and 10D of core 11 and a secondary winding N.sub.2 is wound spreading over legs 10A and 10C of core 11, while a control winding N.sub.c is wound spreading over legs 10A and 10B of core 12. Therefore, windings N.sub.1 and N.sub.2 are in a transformer-coupling mode with coupling factor of about 0.5 to 0.6, while windings N.sub.1, N.sub.2 and winding N.sub.c are in an orthogonal-coupling mode. Control winding N.sub.c is connected in parallel with a control voltage source E.sub.c.
Transformer 10 as mentioned above will have a magnetic flux distribution mode shown in FIGS. 2A and 2B, by way of example. That is, let it be assumed that an exciting current of winding N.sub.1 and its number of turns are I.sub.1 and N.sub.1, a current of winding N.sub.2 and its number of turns are I.sub.2 and N.sub.2, a load current obtained from winding N.sub.2 is I.sub.L, and a total exciting current is I, respectively. Then, a total magnetomotive force NI of transformer 10 is expressed as follows: EQU NI=N.sub.1 I.sub.1 +N.sub.2 I.sub.2 +N.sub.2 I.sub.L
Let it further be assumed that this magnetomotive force NI is caused to produce magnetic flux +.phi..sub.s during the period of positive half cycle of output voltage E.sub.o (refer to FIG. 2A) while magnetic flux -.phi..sub.s during the period of negative half cycle thereof (refer to FIG. 2B), and control winding N.sub.c and control current I.sub.c flowing therethrough are caused to produce magnetic flux .phi..sub.c, respectively. In this case, magnetic fluxes .phi..sub.s and .phi..sub.c are decreased from each other at legs 10A and 10D but added to each other at legs 10B and 10C during the period of positive half cycle (FIG. 2A), and reverse relation therebetween is obtained during the period of negative half cycle (FIG. 2B).
Accordingly, in the B-H characteristic curve (magnetization curve) of FIG. 3, at the peak time point during the period of positive half cycle the operating point of legs 10A, 10D is expressed by 1 and that of legs 10B, 10C is expressed by 2 , while at the peak time point during the period of negative half cycle the operating point of legs 10B, 10C is expressed by 3 and that of legs 10A, 10D is expressed by 4 , respectively. Accordingly, the operating region of legs 10A, 10D corresponds to a section indicated by arrow 1A and the operating region of legs 10B, 10C corresponds to a section indicated by arrow 1B. Output voltage E.sub.o during the period of positive half cycle is determined by magnetic flux density +B.sub.s of legs 10, 10D at point 1 , and output voltage E.sub.o during the period of negative half cycle is determined by magnetic flux density-B.sub.s of legs 10B, 10C at point 3 .
The positions of points 1 and 3 are changed by magnetic flux .phi..sub.c, which is in turn changed according to control current I.sub.c, so that if current I.sub.c is controlled, output voltage E.sub.o can also be controlled.
FIG. 4 shows an equivalent circuit of transformer 10. In this circuit, output voltage E.sub.o (t) is expressed as follows: ##EQU1## where L.sub.2 .multidot.i(t)=N.sub.2 .multidot..PHI. and L.sub.2 is inductance of N.sub.2. In the above equation, the first term represents a voltage induced by transformer coupling, and the second term represents a voltage induced by parametric coupling. In other words, output voltage E.sub.o (t) contains the voltage caused by transformer coupling and the voltage caused by parametric coupling. The ratio between both voltages depends upon the coupling factor of windings N.sub.1 and N.sub.2, or the shape of core and winding method of windings.
Referring to a graph of FIG. 5, if magnetic flux at I.sub.c =0 is taken as .PHI..sub.1, magnetic flux when .phi..sub.s and .phi..sub.c are added to each other is as .PHI..sub.2, magnetic flux when decreased from each other is as .PHI..sub.3, and the variations of .PHI..sub.2 and .PHI..sub.3 from .PHI..sub.1 are as .DELTA..PHI..sub.2, .DELTA..PHI..sub.3, respectively, an output voltage e.sub.o at I.sub.c =0 is given by the following equation: ##EQU2##
Further, when magnetic flux .PHI..sub.3 is in non-linear region at I.sub.c .noteq.0, an output voltage e.sub.os is given as follows: ##EQU3## Because of non-linearity of B-H curve, .DELTA..PHI..sub.3 &gt;&gt;.DELTA..PHI..sub.2 is obtained. Therefore, the following relation is given: ##EQU4## If a point 5 corresponding to .PHI..sub.1 and point 2 corresponding to .PHI..sub.2 are assumed to be in saturated region, .DELTA..PHI..sub.2 .congruent.0 is obtained, so that the following equation can be given: ##EQU5## According to the above equation, if flux variation .DELTA..PHI..sub.3 is controlled by control current I.sub.c, maximum flux density B.sub.s of transformer 10 is controlled with the result that output voltage E.sub.o can be controlled. If the influence of temperature variation of maximum flux density B.sub.s, variation of input voltage, load variation or the like is compensated for by control current I.sub.c, output voltage E.sub.o can be stabilized.
In general, however, the iron loss of a transformer is proportional to the volume of a magnetic core, exciting frequency, and magnetic flux density, while the copper loss thereof is proportional to the number of turns of windings and the volume of core, and the total loss W.sub.t is given as follows: EQU W.sub.t =W.sub.f +W.sub.c
where W.sub.f is iron loss and W.sub.c is copper loss.
Then, if the temperature rise of the transformer is taken as .DELTA.T and the output thereof as P.sub.o, they are expressed as follows: EQU .DELTA.T=.alpha.Wt/A EQU P.sub.o =.beta.SN.sub.a fB.sub.s F.sub.s J
where
.alpha.: constant based upon heat transfer coefficient, PA1 A: total radiating area of transformer, PA1 .beta.: constant based upon form factor, PA1 S: effective sectional area of core, PA1 N.sub.a : effective sectional area of winding, PA1 f: exciting frequency, PA1 B.sub.s : maximum magnetic flux density, PA1 F.sub.s : space factor of winding, and PA1 J: current density of winding
Accordingly, when output P.sub.o of transformer 10 is constant, as maximum flux density B.sub.s is increased, (SN.sub.a) becomes small and hence transformer 10 can be made compact. However, if transformer 10 is made compact, sectional area S becomes small so that temperature rise .DELTA.T is increased due to loss W.sub.t. Such an increase of temperature rise .DELTA.T results in undesirable reliability reduction. Accordingly, a prior art has a drawback that a power supply system becomes large and heavy for the purpose of radiation.